We evaluate the characteristic Hubble time \(1/H\)  as a function of temperature required as reference for the following results. In the Universe epoch of interest \(10< T< 150\)  MeV the Universe is radiation-dominated. This observation helps to relate the cosmological time to the ambient temperature. However, in this work all that matters is that we can express the Hubble expansion rate as a function of temperature. This is achieved remembering that the Hubble parameter can be written as [1]}

H2=8GN3 tot,

where \(G_\mathrm {N}\)  is the Newtonian constant of gravitation and \(\rho _{tot}\)  is the energy density (here of for most part of relativistic `radiation like' particle species) in the early Universe. In our calculation we include

Photon:
